Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.9 | ||
Root | \(-1.64368 - 0.546177i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.h.1949.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.64368 | + | 0.546177i | 0.948980 | + | 0.315336i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41433 | + | 1.08214i | −0.912531 | + | 0.409009i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.40338 | + | 1.79548i | 0.801127 | + | 0.598494i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17086 | + | 0.675999i | −0.353029 | + | 0.203821i | −0.666018 | − | 0.745935i | \(-0.732003\pi\) |
0.312990 | + | 0.949757i | \(0.398669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.94296 | 1.37093 | 0.685466 | − | 0.728105i | \(-0.259599\pi\) | ||||
0.685466 | + | 0.728105i | \(0.259599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.97280 | + | 2.87105i | −1.20608 | + | 0.696332i | −0.961901 | − | 0.273398i | \(-0.911852\pi\) |
−0.244181 | + | 0.969730i | \(0.578519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.84694 | − | 1.64368i | −0.653133 | − | 0.377087i | 0.136523 | − | 0.990637i | \(-0.456407\pi\) |
−0.789656 | + | 0.613550i | \(0.789741\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.55943 | + | 0.460035i | −0.994948 | + | 0.100388i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.50270 | + | 4.33480i | −0.521849 | + | 0.903868i | 0.477828 | + | 0.878453i | \(0.341424\pi\) |
−0.999677 | + | 0.0254150i | \(0.991909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.96974 | + | 4.26388i | 0.571527 | + | 0.820583i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68630i | 1.05592i | 0.849270 | + | 0.527959i | \(0.177043\pi\) | ||||
−0.849270 | + | 0.527959i | \(0.822957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.45160 | + | 1.41543i | −0.440320 | + | 0.254219i | −0.703733 | − | 0.710464i | \(-0.748485\pi\) |
0.263414 | + | 0.964683i | \(0.415152\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.29374 | + | 0.471628i | −0.399289 | + | 0.0820998i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.33498 | + | 1.92545i | 0.548267 | + | 0.316542i | 0.748423 | − | 0.663222i | \(-0.230811\pi\) |
−0.200156 | + | 0.979764i | \(0.564145\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.12466 | + | 2.69973i | 1.30099 | + | 0.432303i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.73802 | 0.583781 | 0.291890 | − | 0.956452i | \(-0.405716\pi\) | ||||
0.291890 | + | 0.956452i | \(0.405716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.06339i | 0.619661i | 0.950792 | + | 0.309830i | \(0.100272\pi\) | ||||
−0.950792 | + | 0.309830i | \(0.899728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.92419 | − | 2.84298i | −0.718266 | − | 0.414691i | 0.0958478 | − | 0.995396i | \(-0.469444\pi\) |
−0.814114 | + | 0.580705i | \(0.802777\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65797 | − | 5.22526i | 0.665424 | − | 0.746466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.74181 | + | 2.00306i | −1.36413 | + | 0.280484i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.730773 | − | 1.26574i | −0.100379 | − | 0.173862i | 0.811462 | − | 0.584406i | \(-0.198672\pi\) |
−0.911841 | + | 0.410544i | \(0.865339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.78172 | − | 4.25662i | −0.500902 | − | 0.563804i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.34239 | − | 7.52123i | −0.565330 | − | 0.979181i | −0.997019 | − | 0.0771582i | \(-0.975415\pi\) |
0.431688 | − | 0.902023i | \(-0.357918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.65306 | + | 0.954394i | 0.211653 | + | 0.122198i | 0.602079 | − | 0.798436i | \(-0.294339\pi\) |
−0.390427 | + | 0.920634i | \(0.627672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.74551 | − | 1.73410i | −0.975842 | − | 0.218477i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.36371 | + | 2.51939i | −0.533113 | + | 0.307793i | −0.742283 | − | 0.670086i | \(-0.766257\pi\) |
0.209170 | + | 0.977879i | \(0.432924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.48121 | + | 5.75812i | −0.780246 | + | 0.693196i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.38259i | 0.401440i | 0.979649 | + | 0.200720i | \(0.0643281\pi\) | ||||
−0.979649 | + | 0.200720i | \(0.935672\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.16364 | + | 14.1398i | 0.955481 | + | 1.65494i | 0.733263 | + | 0.679945i | \(0.237996\pi\) |
0.222218 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.09533 | − | 2.89912i | 0.238785 | − | 0.330385i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.41693 | − | 4.18625i | 0.271926 | − | 0.470990i | −0.697429 | − | 0.716654i | \(-0.745673\pi\) |
0.969355 | + | 0.245664i | \(0.0790059\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.55248 | + | 8.63046i | 0.283609 | + | 0.958940i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.6525i | 1.82785i | 0.405879 | + | 0.913927i | \(0.366965\pi\) | ||||
−0.405879 | + | 0.913927i | \(0.633035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.10572 | + | 9.34646i | −0.332969 | + | 1.00205i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.08150 | + | 13.9976i | −0.856637 | + | 1.48374i | 0.0184813 | + | 0.999829i | \(0.494117\pi\) |
−0.875118 | + | 0.483909i | \(0.839216\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.9339 | + | 5.34895i | −1.25102 | + | 0.560723i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.80272 | + | 0.987510i | −0.498019 | + | 0.102400i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0577 | 1.22427 | 0.612137 | − | 0.790751i | \(-0.290310\pi\) | ||||
0.612137 | + | 0.790751i | \(0.290310\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.02778 | − | 0.477584i | −0.404807 | − | 0.0479990i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.01683 | − | 15.6176i | −0.897208 | − | 1.55401i | −0.831048 | − | 0.556201i | \(-0.812258\pi\) |
−0.0661605 | − | 0.997809i | \(-0.521075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.308083 | + | 0.533615i | −0.0303563 | + | 0.0525787i | −0.880804 | − | 0.473480i | \(-0.842998\pi\) |
0.850448 | + | 0.526059i | \(0.176331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.85503 | − | 15.3374i | 0.856048 | − | 1.48272i | −0.0196209 | − | 0.999807i | \(-0.506246\pi\) |
0.875669 | − | 0.482912i | \(-0.160421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.855282 | − | 1.48139i | −0.0819211 | − | 0.141892i | 0.822154 | − | 0.569265i | \(-0.192772\pi\) |
−0.904075 | + | 0.427374i | \(0.859439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43001 | + | 4.98632i | 0.420478 | + | 0.473280i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1214 | −1.23436 | −0.617180 | − | 0.786822i | \(-0.711725\pi\) | ||||
−0.617180 | + | 0.786822i | \(0.711725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.8798 | + | 8.87501i | 1.09829 | + | 0.820495i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.89912 | − | 12.3129i | 0.815781 | − | 1.12872i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.58605 | + | 7.94327i | −0.416914 | + | 0.722116i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.14412 | + | 2.04162i | 0.553996 | + | 0.184087i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5324i | 1.37828i | 0.724629 | + | 0.689139i | \(0.242011\pi\) | ||||
−0.724629 | + | 0.689139i | \(0.757989\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.21933 | + | 6.67892i | −0.195401 | + | 0.588046i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.47822 | − | 7.75651i | 0.391264 | − | 0.677689i | −0.601353 | − | 0.798984i | \(-0.705371\pi\) |
0.992617 | + | 0.121295i | \(0.0387046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.65214 | + | 0.887614i | 0.750235 | + | 0.0769659i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.73923 | + | 13.4047i | 0.661207 | + | 1.14524i | 0.980299 | + | 0.197520i | \(0.0632888\pi\) |
−0.319092 | + | 0.947724i | \(0.603378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.1547i | − | 1.70950i | −0.519044 | − | 0.854748i | \(-0.673712\pi\) | ||
0.519044 | − | 0.854748i | \(-0.326288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.54103 | − | 7.36243i | −0.550854 | − | 0.620029i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.78754 | + | 3.34144i | −0.483978 | + | 0.279425i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.5101 | − | 6.04459i | 0.866861 | − | 0.498549i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.24947 | − | 0.721384i | −0.102361 | − | 0.0590981i | 0.447946 | − | 0.894061i | \(-0.352156\pi\) |
−0.550307 | + | 0.834963i | \(0.685489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.12108 | − | 14.0661i | −0.660884 | − | 1.14468i | −0.980384 | − | 0.197098i | \(-0.936848\pi\) |
0.319500 | − | 0.947586i | \(-0.396485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.1065 | − | 2.02836i | −1.38298 | − | 0.163983i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.11876 | − | 15.7942i | −0.727756 | − | 1.26051i | −0.957829 | − | 0.287338i | \(-0.907230\pi\) |
0.230073 | − | 0.973173i | \(-0.426103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.509842 | − | 2.47960i | −0.0404331 | − | 0.196645i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.35150 | − | 13.1739i | 0.106513 | − | 1.03825i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0669 | + | 12.1630i | 1.65009 | + | 0.952679i | 0.977033 | + | 0.213087i | \(0.0683517\pi\) |
0.673055 | + | 0.739592i | \(0.264982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.5007i | 0.967336i | 0.875252 | + | 0.483668i | \(0.160696\pi\) | ||||
−0.875252 | + | 0.483668i | \(0.839304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4329 | 0.879453 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.89108 | − | 9.06203i | −0.297558 | − | 0.692991i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8534 | + | 7.42089i | 0.977223 | + | 0.564200i | 0.901431 | − | 0.432923i | \(-0.142518\pi\) |
0.0757927 | + | 0.997124i | \(0.475851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.02957 | − | 14.7342i | −0.227717 | − | 1.10749i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.93533 | − | 5.73617i | 0.742602 | − | 0.428741i | −0.0804127 | − | 0.996762i | \(-0.525624\pi\) |
0.823015 | + | 0.568020i | \(0.192291\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.91099i | − | 0.439361i | −0.975572 | − | 0.219680i | \(-0.929499\pi\) | ||
0.975572 | − | 0.219680i | \(-0.0705014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.19584 | + | 2.47158i | 0.162321 | + | 0.182705i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.88165 | − | 6.72322i | 0.283854 | − | 0.491650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.7840 | − | 7.08073i | −0.857162 | − | 0.515048i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.15764 | − | 5.28716i | −0.662623 | − | 0.382566i | 0.130652 | − | 0.991428i | \(-0.458293\pi\) |
−0.793276 | + | 0.608862i | \(0.791626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4483 | − | 6.03231i | 0.752082 | − | 0.434215i | −0.0743635 | − | 0.997231i | \(-0.523693\pi\) |
0.826446 | + | 0.563016i | \(0.190359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2423 | −1.22846 | −0.614231 | − | 0.789126i | \(-0.710534\pi\) | ||||
−0.614231 | + | 0.789126i | \(0.710534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.46400 | + | 1.42259i | −0.174668 | + | 0.100845i | −0.584785 | − | 0.811188i | \(-0.698821\pi\) |
0.410117 | + | 0.912033i | \(0.365488\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.54859 | + | 1.75772i | −0.602971 | + | 0.123980i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.15334 | − | 13.7286i | −0.431880 | − | 0.963558i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.7980 | + | 5.92462i | −0.959027 | + | 0.411790i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.44451 | 0.307433 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4677 | 1.54674 | 0.773372 | − | 0.633953i | \(-0.218569\pi\) | ||||
0.773372 | + | 0.633953i | \(0.218569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.84749 | + | 5.55991i | −0.126588 | + | 0.380958i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.38727 | − | 6.07027i | 0.297828 | − | 0.412077i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.69557 | + | 27.7002i | 0.384871 | + | 1.87180i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.5804 | + | 14.1915i | −1.65346 | + | 0.954623i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.27620 | 0.353321 | 0.176660 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176660 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.8090 | + | 6.24055i | −0.717416 | + | 0.414200i | −0.813801 | − | 0.581144i | \(-0.802605\pi\) |
0.0963851 | + | 0.995344i | \(0.469272\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0882 | + | 8.13380i | 0.930971 | + | 0.537496i | 0.887119 | − | 0.461542i | \(-0.152703\pi\) |
0.0438526 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.02749 | − | 3.62080i | 0.330784 | − | 0.238231i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.41551 | − | 7.64788i | 0.289269 | − | 0.501029i | −0.684366 | − | 0.729139i | \(-0.739921\pi\) |
0.973636 | + | 0.228109i | \(0.0732543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.25911 | − | 5.56079i | 0.406573 | − | 0.361212i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.3333i | − | 0.797773i | −0.917000 | − | 0.398886i | \(-0.869397\pi\) | ||
0.917000 | − | 0.398886i | \(-0.130603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.88815 | − | 3.97688i | 0.443705 | − | 0.256173i | −0.261463 | − | 0.965214i | \(-0.584205\pi\) |
0.705168 | + | 0.709040i | \(0.250872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.518295 | + | 15.5798i | −0.0332486 | + | 0.999447i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0723 | − | 8.12466i | −0.895401 | − | 0.516960i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.09524 | + | 27.3715i | −0.576387 | + | 1.73460i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.64756 | 0.482710 | 0.241355 | − | 0.970437i | \(-0.422408\pi\) | ||||
0.241355 | + | 0.970437i | \(0.422408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.76728i | − | 0.425455i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.8118 | + | 13.7478i | 1.48534 | + | 0.857563i | 0.999861 | − | 0.0166841i | \(-0.00531095\pi\) |
0.485482 | + | 0.874247i | \(0.338644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.1353 | − | 1.03977i | −0.629779 | − | 0.0646084i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2096 | + | 13.6663i | −0.631961 | + | 0.845925i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.51115 | − | 16.4738i | −0.586483 | − | 1.01582i | −0.994689 | − | 0.102928i | \(-0.967179\pi\) |
0.408206 | − | 0.912890i | \(-0.366155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.9286 | + | 18.5936i | −1.28081 | + | 1.13791i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.46010 | + | 7.72512i | 0.271937 | + | 0.471009i | 0.969358 | − | 0.245653i | \(-0.0790024\pi\) |
−0.697421 | + | 0.716662i | \(0.745669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.53123 | + | 3.77081i | 0.396744 | + | 0.229060i | 0.685078 | − | 0.728470i | \(-0.259768\pi\) |
−0.288334 | + | 0.957530i | \(0.593101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.5371 | + | 2.27393i | −1.36401 | + | 0.137625i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.53903 | − | 0.888562i | 0.0924716 | − | 0.0533885i | −0.453051 | − | 0.891485i | \(-0.649664\pi\) |
0.545523 | + | 0.838096i | \(0.316331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.43350 | − | 0.999983i | −0.504900 | − | 0.0598674i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3819i | 1.51416i | 0.653324 | + | 0.757079i | \(0.273374\pi\) | ||||
−0.653324 | + | 0.757079i | \(0.726626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.06987 | − | 13.9774i | −0.479704 | − | 0.830872i | 0.520025 | − | 0.854151i | \(-0.325923\pi\) |
−0.999729 | + | 0.0232795i | \(0.992589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.02481 | + | 4.04504i | −0.532718 | + | 0.238771i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.98584 | − | 13.8319i | 0.469755 | − | 0.813640i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.8190 | + | 6.58564i | 1.16181 | + | 0.386057i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.5542i | − | 1.14237i | −0.820821 | − | 0.571186i | \(-0.806484\pi\) | ||
0.820821 | − | 0.571186i | \(-0.193516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.35954 | − | 2.98488i | −0.369018 | − | 0.173200i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.3707 | + | 21.4268i | −0.715419 | + | 1.23914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.39713 | − | 9.81035i | −0.253447 | − | 0.565459i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.29082 | − | 30.5952i | −0.361398 | − | 1.75765i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.8231 | 0.674777 | 0.337389 | − | 0.941365i | \(-0.390456\pi\) | ||||
0.337389 | + | 0.941365i | \(0.390456\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.797839 | + | 0.708826i | −0.0453875 | + | 0.0403237i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1689 | + | 19.3451i | 0.633331 | + | 1.09696i | 0.986866 | + | 0.161540i | \(0.0516462\pi\) |
−0.353535 | + | 0.935421i | \(0.615020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.65398 | − | 11.5250i | 0.376105 | − | 0.651433i | −0.614387 | − | 0.789005i | \(-0.710596\pi\) |
0.990492 | + | 0.137572i | \(0.0439298\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9392 | − | 29.3395i | 0.951400 | − | 1.64787i | 0.209001 | − | 0.977915i | \(-0.432979\pi\) |
0.742399 | − | 0.669958i | \(-0.233688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.84393 | − | 6.65788i | −0.215219 | − | 0.372770i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.9318 | − | 20.3733i | 1.27993 | − | 1.13713i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.8764 | 1.05031 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.596709 | − | 2.90207i | −0.0329981 | − | 0.160485i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.9651 | + | 1.53525i | 0.825052 | + | 0.0846413i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.989824 | − | 1.71443i | 0.0544057 | − | 0.0942334i | −0.837540 | − | 0.546376i | \(-0.816007\pi\) |
0.891946 | + | 0.452143i | \(0.149340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.55811 | + | 10.6155i | 0.249783 | + | 0.581725i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.0217i | 0.654862i | 0.944875 | + | 0.327431i | \(0.106183\pi\) | ||||
−0.944875 | + | 0.327431i | \(0.893817\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.5674 | − | 7.16662i | −1.17138 | − | 0.389237i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.91366 | − | 3.31455i | 0.103630 | − | 0.179493i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.59143 | + | 17.6560i | −0.301909 | + | 0.953337i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.33186 | − | 12.6992i | −0.393595 | − | 0.681726i | 0.599326 | − | 0.800505i | \(-0.295435\pi\) |
−0.992921 | + | 0.118779i | \(0.962102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 25.0573i | − | 1.34129i | −0.741780 | − | 0.670644i | \(-0.766018\pi\) | ||
0.741780 | − | 0.670644i | \(-0.233982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6793 | + | 21.0762i | 0.783525 | + | 1.12496i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.72669 | − | 3.88365i | 0.358025 | − | 0.206706i | −0.310189 | − | 0.950675i | \(-0.600392\pi\) |
0.668214 | + | 0.743969i | \(0.267059\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.3523 | − | 15.3780i | 1.13009 | − | 0.813890i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.86952 | − | 2.23407i | −0.204225 | − | 0.117910i | 0.394399 | − | 0.918939i | \(-0.370953\pi\) |
−0.598625 | + | 0.801030i | \(0.704286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.09662 | − | 7.09555i | −0.215612 | − | 0.373450i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.8764 | + | 10.5514i | −0.623352 | + | 0.553806i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.842240 | − | 1.45880i | −0.0439646 | − | 0.0761489i | 0.843206 | − | 0.537591i | \(-0.180666\pi\) |
−0.887170 | + | 0.461442i | \(0.847332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.98389 | + | 6.71155i | 0.467682 | + | 0.349389i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13402 | + | 2.26511i | 0.162710 | + | 0.117599i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.9914 | − | 6.92322i | −0.620890 | − | 0.358471i | 0.156325 | − | 0.987706i | \(-0.450035\pi\) |
−0.777215 | + | 0.629235i | \(0.783368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.1072i | 1.44759i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.15603 | 0.110748 | 0.0553739 | − | 0.998466i | \(-0.482365\pi\) | ||||
0.0553739 | + | 0.998466i | \(0.482365\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.48345 | + | 25.5303i | −0.434620 | + | 1.30796i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.23197 | + | 1.86598i | 0.165146 | + | 0.0953471i | 0.580295 | − | 0.814406i | \(-0.302937\pi\) |
−0.415149 | + | 0.909753i | \(0.636271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.29574 | + | 9.76587i | −0.370863 | + | 0.496427i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.9512 | + | 6.90001i | −0.605948 | + | 0.349844i | −0.771378 | − | 0.636377i | \(-0.780432\pi\) |
0.165430 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 28.7415i | − | 1.45352i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.5972 | − | 10.3033i | 0.585001 | − | 0.519734i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.17565 | + | 14.1606i | −0.410324 | + | 0.710702i | −0.994925 | − | 0.100619i | \(-0.967918\pi\) |
0.584601 | + | 0.811321i | \(0.301251\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.7366 | + | 6.18456i | 0.687688 | + | 0.309615i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.9669 | + | 6.90910i | 0.597599 | + | 0.345024i | 0.768096 | − | 0.640334i | \(-0.221204\pi\) |
−0.170497 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.1182 | + | 6.99642i | −0.603648 | + | 0.348516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.20641 | −0.258072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.26987 | − | 4.77461i | 0.408919 | − | 0.236089i | −0.281406 | − | 0.959589i | \(-0.590801\pi\) |
0.690325 | + | 0.723499i | \(0.257467\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.39947 | + | 26.2601i | 0.266336 | + | 1.29532i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.6229 | + | 13.4597i | 0.916375 | + | 0.662307i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0080 | − | 33.1278i | 0.539065 | − | 1.62228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.71886 | 0.474797 | 0.237399 | − | 0.971412i | \(-0.423705\pi\) | ||||
0.237399 | + | 0.971412i | \(0.423705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.8713 | 1.69953 | 0.849763 | − | 0.527165i | \(-0.176745\pi\) | ||||
0.849763 | + | 0.527165i | \(0.176745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.73017 | − | 15.6741i | −0.327232 | − | 0.762099i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.02381 | − | 0.515388i | −0.243119 | − | 0.0249414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.3379 | + | 2.33124i | −0.547399 | + | 0.112553i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.57279 | − | 0.908052i | 0.0757587 | − | 0.0437393i | −0.461642 | − | 0.887066i | \(-0.652740\pi\) |
0.537401 | + | 0.843327i | \(0.319406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.6773 | 0.513117 | 0.256558 | − | 0.966529i | \(-0.417411\pi\) | ||||
0.256558 | + | 0.966529i | \(0.417411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.2501 | − | 8.22728i | 0.681673 | − | 0.393564i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.6759 | − | 15.4013i | −1.27317 | − | 0.735066i | −0.297588 | − | 0.954694i | \(-0.596182\pi\) |
−0.975584 | + | 0.219628i | \(0.929516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5767 | − | 4.19499i | 0.979845 | − | 0.199761i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.26640 | + | 14.3178i | −0.392749 | + | 0.680260i | −0.992811 | − | 0.119693i | \(-0.961809\pi\) |
0.600062 | + | 0.799953i | \(0.295142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.65974 | − | 1.86816i | −0.0785028 | − | 0.0883610i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.59098i | 0.122276i | 0.998129 | + | 0.0611380i | \(0.0194730\pi\) | ||||
−0.998129 | + | 0.0611380i | \(0.980527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.37671 | + | 2.52690i | −0.206091 | + | 0.118987i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.66588 | − | 27.5558i | −0.266206 | − | 1.29468i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2040 | − | 11.0874i | −0.898323 | − | 0.518647i | −0.0216672 | − | 0.999765i | \(-0.506897\pi\) |
−0.876656 | + | 0.481118i | \(0.840231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −27.0097 | − | 12.6771i | −1.26071 | − | 0.591718i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.5304 | 1.42194 | 0.710971 | − | 0.703221i | \(-0.248256\pi\) | ||||
0.710971 | + | 0.703221i | \(0.248256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.54824i | 0.164901i | 0.996595 | + | 0.0824504i | \(0.0262746\pi\) | ||||
−0.996595 | + | 0.0824504i | \(0.973725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.7157 | − | 17.1564i | −1.37508 | − | 0.793901i | −0.383515 | − | 0.923534i | \(-0.625287\pi\) |
−0.991562 | + | 0.129633i | \(0.958620\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.80912 | − | 10.8048i | 0.360592 | − | 0.498918i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.36193 | − | 30.9410i | −0.293142 | − | 1.42569i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.74684 | − | 4.75767i | −0.126300 | − | 0.218758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.516282 | − | 4.35414i | 0.0236389 | − | 0.199362i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.78624 | − | 16.9503i | −0.447145 | − | 0.774477i | 0.551054 | − | 0.834469i | \(-0.314226\pi\) |
−0.998199 | + | 0.0599923i | \(0.980892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4847 | + | 9.51743i | 0.751637 | + | 0.433958i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.41671 | − | 20.9155i | 0.428475 | − | 0.951689i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.8468 | + | 12.6133i | −0.989973 | + | 0.571561i | −0.905266 | − | 0.424844i | \(-0.860329\pi\) |
−0.0847071 | + | 0.996406i | \(0.526995\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.9842 | + | 31.4984i | 1.26549 | + | 1.42441i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.6556i | 1.74450i | 0.489057 | + | 0.872252i | \(0.337341\pi\) | ||||
−0.489057 | + | 0.872252i | \(0.662659\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.3256 | − | 28.2768i | −0.735269 | − | 1.27352i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.66042 | − | 8.16669i | −0.164192 | − | 0.366326i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.80910 | − | 4.86551i | 0.125753 | − | 0.217810i | −0.796274 | − | 0.604936i | \(-0.793199\pi\) |
0.922027 | + | 0.387126i | \(0.126532\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.82761 | + | 20.5472i | −0.305035 | + | 0.917982i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.8655i | − | 1.15329i | −0.816996 | − | 0.576644i | \(-0.804362\pi\) | ||
0.816996 | − | 0.576644i | \(-0.195638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.7920 | + | 6.24438i | 0.834584 | + | 0.277323i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.2306 | − | 26.3801i | 0.675082 | − | 1.16928i | −0.301362 | − | 0.953510i | \(-0.597441\pi\) |
0.976445 | − | 0.215767i | \(-0.0692253\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0109 | − | 25.3040i | −1.54879 | − | 1.11939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.44622 | − | 17.0203i | −0.0638524 | − | 0.751465i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.68740 | 0.338092 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.0737 | + | 19.2178i | 0.749453 | + | 0.843568i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.6182 | + | 18.3913i | 0.465192 | + | 0.805737i | 0.999210 | − | 0.0397366i | \(-0.0126519\pi\) |
−0.534018 | + | 0.845473i | \(0.679319\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.19077 | − | 10.7227i | 0.270704 | − | 0.468872i | −0.698339 | − | 0.715768i | \(-0.746077\pi\) |
0.969042 | + | 0.246895i | \(0.0794103\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.12754 | − | 14.0773i | 0.354041 | − | 0.613217i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.02699 | − | 1.77880i | −0.0446518 | − | 0.0773392i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.06784 | − | 25.8731i | 0.133133 | − | 1.12280i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.4769 | 0.800323 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.4635 | − | 4.00198i | 0.839912 | − | 0.172698i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.92158 | + | 9.26685i | −0.0827682 | + | 0.399151i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.93001 | + | 12.0031i | −0.297944 | + | 0.516055i | −0.975665 | − | 0.219264i | \(-0.929634\pi\) |
0.677721 | + | 0.735319i | \(0.262968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.22845 | − | 9.71579i | 0.138546 | − | 0.416945i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 17.7100i | − | 0.757226i | −0.925555 | − | 0.378613i | \(-0.876401\pi\) | ||
0.925555 | − | 0.378613i | \(-0.123599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.25933 | + | 5.26181i | 0.0964260 | + | 0.224569i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.34646 | − | 16.1885i | 0.398173 | − | 0.689655i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.30518 | + | 12.7224i | −0.0555020 | + | 0.541013i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.73857 | + | 3.01129i | 0.0736656 | + | 0.127593i | 0.900505 | − | 0.434845i | \(-0.143197\pi\) |
−0.826840 | + | 0.562438i | \(0.809864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.0852i | 0.849512i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0523 | − | 8.93076i | 0.424407 | − | 0.377057i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4425 | + | 6.02897i | −0.440098 | + | 0.254091i | −0.703639 | − | 0.710557i | \(-0.748443\pi\) |
0.263541 | + | 0.964648i | \(0.415110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.5019 | − | 18.0746i | −0.651017 | − | 0.759064i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.8065 | − | 6.81650i | −0.494955 | − | 0.285762i | 0.231673 | − | 0.972794i | \(-0.425580\pi\) |
−0.726628 | + | 0.687031i | \(0.758913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0474 | + | 38.1873i | 0.922657 | + | 1.59809i | 0.795287 | + | 0.606233i | \(0.207320\pi\) |
0.127369 | + | 0.991855i | \(0.459347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.1645 | − | 13.6921i | −0.508180 | − | 0.571996i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.49934 | + | 6.06103i | 0.145679 | + | 0.252324i | 0.929626 | − | 0.368504i | \(-0.120130\pi\) |
−0.783947 | + | 0.620828i | \(0.786797\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.4683 | − | 4.20859i | 0.850635 | − | 0.174903i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0203 | − | 40.2047i | −0.747608 | − | 1.66797i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.71127 | + | 0.988003i | 0.0708736 | + | 0.0409189i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.9161i | 1.23477i | 0.786661 | + | 0.617385i | \(0.211808\pi\) | ||||
−0.786661 | + | 0.617385i | \(0.788192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.30607 | 0.383450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3408 | − | 9.41734i | −1.16579 | − | 0.387378i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8583 | + | 12.0426i | 0.856549 | + | 0.494529i | 0.862855 | − | 0.505451i | \(-0.168674\pi\) |
−0.00630583 | + | 0.999980i | \(0.502007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.82702 | + | 0.992506i | −0.197557 | + | 0.0406206i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.14773 | + | 2.97205i | −0.210331 | + | 0.121434i | −0.601465 | − | 0.798899i | \(-0.705416\pi\) |
0.391134 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.9992i | − | 1.91714i | −0.284863 | − | 0.958568i | \(-0.591948\pi\) | ||
0.284863 | − | 0.958568i | \(-0.408052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.0112 | − | 1.77992i | −0.611303 | − | 0.0724839i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.97322 | + | 8.61387i | −0.201857 | + | 0.349626i | −0.949127 | − | 0.314894i | \(-0.898031\pi\) |
0.747270 | + | 0.664521i | \(0.231364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.61589 | − | 25.9262i | −0.106001 | − | 1.05058i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.3401 | − | 14.0528i | −0.984694 | − | 0.568513i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.1873 | + | 16.2739i | −1.13847 | + | 0.657298i | −0.946052 | − | 0.324014i | \(-0.894967\pi\) |
−0.192421 | + | 0.981312i | \(0.561634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.69843 | 0.309927 | 0.154964 | − | 0.987920i | \(-0.450474\pi\) | ||||
0.154964 | + | 0.987920i | \(0.450474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.76170 | + | 1.59447i | −0.111002 | + | 0.0640872i | −0.554473 | − | 0.832202i | \(-0.687080\pi\) |
0.443471 | + | 0.896289i | \(0.353747\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −25.9154 | + | 2.20205i | −1.03995 | + | 0.0883650i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.36414 | − | 42.5400i | 0.174845 | − | 1.70433i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.30536 | + | 2.42749i | 0.291748 | + | 0.0969446i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.1122 | −0.881673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.97461 | 0.317464 | 0.158732 | − | 0.987322i | \(-0.449259\pi\) | ||||
0.158732 | + | 0.987322i | \(0.449259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 36.9298 | + | 12.2714i | 1.46783 | + | 0.487743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.0242 | − | 25.8283i | 0.912251 | − | 1.02335i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.07339 | + | 8.12966i | −0.240259 | + | 0.321604i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7774 | − | 13.7279i | 0.939152 | − | 0.542219i | 0.0494573 | − | 0.998776i | \(-0.484251\pi\) |
0.889694 | + | 0.456557i | \(0.150917\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.0919 | 1.14727 | 0.573637 | − | 0.819110i | \(-0.305532\pi\) | ||||
0.573637 | + | 0.819110i | \(0.305532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.4122 | − | 21.5999i | 1.47082 | − | 0.849181i | 0.471361 | − | 0.881940i | \(-0.343763\pi\) |
0.999463 | + | 0.0327597i | \(0.0104296\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1687 | + | 5.87089i | 0.399156 | + | 0.230453i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.5267 | − | 7.58137i | 0.412575 | − | 0.297137i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.62080 | + | 6.27142i | −0.141693 | + | 0.245420i | −0.928134 | − | 0.372246i | \(-0.878588\pi\) |
0.786441 | + | 0.617665i | \(0.211921\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.76750 | + | 48.6411i | −0.225012 | + | 1.89767i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.29324i | − | 0.206196i | −0.994671 | − | 0.103098i | \(-0.967125\pi\) | ||
0.994671 | − | 0.103098i | \(-0.0328755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2638 | − | 24.9783i | 1.68276 | − | 0.971545i | 0.722954 | − | 0.690896i | \(-0.242784\pi\) |
0.959810 | − | 0.280649i | \(-0.0905497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.1534 | + | 9.90105i | −1.87012 | + | 0.384525i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.6490 | − | 14.2311i | −0.954411 | − | 0.551030i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.67240 | + | 2.88174i | 0.335294 | + | 0.111415i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.58068 | −0.0996259 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.8855i | − | 0.843625i | −0.906683 | − | 0.421812i | \(-0.861394\pi\) | ||
0.906683 | − | 0.421812i | \(-0.138606\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.9033 | − | 6.87236i | −0.457480 | − | 0.264126i | 0.253504 | − | 0.967334i | \(-0.418417\pi\) |
−0.710984 | + | 0.703208i | \(0.751750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1113 | + | 13.0481i | −1.11719 | + | 0.500739i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.1749 | + | 4.35388i | −0.811425 | + | 0.166841i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.4513 | + | 37.1547i | 0.820811 | + | 1.42169i | 0.905079 | + | 0.425243i | \(0.139811\pi\) |
−0.0842682 | + | 0.996443i | \(0.526855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.7139 | + | 21.0640i | 0.713982 | + | 0.803642i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.61218 | − | 6.25649i | −0.137613 | − | 0.238353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.5494 | − | 11.8642i | −0.781735 | − | 0.451335i | 0.0553098 | − | 0.998469i | \(-0.482385\pi\) |
−0.837045 | + | 0.547134i | \(0.815719\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.2412 | − | 3.20555i | 0.389031 | − | 0.121769i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5884 | + | 10.7320i | −0.704087 | + | 0.406505i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.4348 | − | 10.1590i | 0.432503 | − | 0.384250i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2721i | − | 0.803436i | −0.915763 | − | 0.401718i | \(-0.868413\pi\) | ||
0.915763 | − | 0.401718i | \(-0.131587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.32966 | − | 10.9633i | −0.238728 | − | 0.413488i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.6700 | + | 27.9486i | 1.45433 | + | 1.05112i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.8069 | + | 39.5026i | −0.856529 | + | 1.48355i | 0.0186897 | + | 0.999825i | \(0.494051\pi\) |
−0.875219 | + | 0.483727i | \(0.839283\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3252 | − | 5.72160i | 0.499733 | − | 0.214577i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 14.1696i | − | 0.530655i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.73615 | − | 20.2720i | 0.251566 | − | 0.757071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.50850 | + | 16.4692i | −0.354607 | + | 0.614198i | −0.987051 | − | 0.160409i | \(-0.948719\pi\) |
0.632443 | + | 0.774607i | \(0.282052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.166370 | − | 1.62171i | 0.00619593 | − | 0.0603956i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.4940 | − | 2.77457i | 0.501848 | − | 0.103187i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0540 | 1.26299 | 0.631496 | − | 0.775379i | \(-0.282441\pi\) | ||||
0.631496 | + | 0.775379i | \(0.282441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.36126 | + | 25.3252i | −0.346714 | + | 0.937971i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6662 | − | 20.2064i | −0.431489 | − | 0.747361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.87885 | − | 6.71837i | 0.143269 | − | 0.248148i | −0.785457 | − | 0.618916i | \(-0.787572\pi\) |
0.928726 | + | 0.370768i | \(0.120905\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.40621 | − | 5.89973i | 0.125469 | − | 0.217319i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.19659 | − | 7.26871i | −0.154374 | − | 0.267384i | 0.778457 | − | 0.627698i | \(-0.216003\pi\) |
−0.932831 | + | 0.360314i | \(0.882669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.6929 | − | 21.0403i | −0.686702 | − | 0.772936i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7540 | −0.541273 | −0.270636 | − | 0.962682i | \(-0.587234\pi\) | ||||
−0.270636 | + | 0.962682i | \(0.587234\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −29.8994 | + | 40.0224i | −1.09396 | + | 1.46434i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.78186 | + | 46.6118i | −0.174725 | + | 1.70316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6067 | + | 35.6918i | −0.751948 | + | 1.30241i | 0.194929 | + | 0.980817i | \(0.437552\pi\) |
−0.946877 | + | 0.321595i | \(0.895781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.5702 | + | 4.17692i | 0.458082 | + | 0.152216i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.8681i | 0.431354i | 0.976465 | + | 0.215677i | \(0.0691958\pi\) | ||||
−0.976465 | + | 0.215677i | \(0.930804\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.69613 | − | 11.1233i | 0.134161 | − | 0.403749i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7705 | + | 30.7795i | −0.644181 | + | 1.11575i | 0.340309 | + | 0.940314i | \(0.389468\pi\) |
−0.984490 | + | 0.175441i | \(0.943865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.66800 | + | 2.65104i | 0.132790 | + | 0.0959739i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.4643 | − | 37.1772i | −0.775029 | − | 1.34239i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.25608i | 0.225600i | 0.993618 | + | 0.112800i | \(0.0359820\pi\) | ||||
−0.993618 | + | 0.112800i | \(0.964018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.6304 | + | 35.6025i | 1.13914 | + | 1.28219i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.3483 | + | 10.0161i | −0.623977 | + | 0.360253i | −0.778416 | − | 0.627749i | \(-0.783976\pi\) |
0.154439 | + | 0.988002i | \(0.450643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0914 | − | 7.24474i | −0.577274 | − | 0.259904i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.6419 | − | 6.14412i | −0.381286 | − | 0.220136i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.28663 | − | 3.96056i | −0.0818220 | − | 0.141720i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.2457 | + | 16.8868i | −0.866469 | + | 0.603486i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.738053 | + | 1.27835i | 0.0263088 | + | 0.0455681i | 0.878880 | − | 0.477043i | \(-0.158291\pi\) |
−0.852571 | + | 0.522611i | \(0.824958\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.63570 | − | 32.2725i | −0.236237 | − | 1.14893i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.6794 | − | 14.1991i | 1.12639 | − | 0.504863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.17101 | + | 4.71754i | 0.290161 | + | 0.167525i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 22.9470i | − | 0.812823i | −0.913690 | − | 0.406411i | \(-0.866780\pi\) | ||
0.913690 | − | 0.406411i | \(-0.133220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.6493 | 1.15505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.5553 | + | 19.1313i | −1.57428 | + | 0.675971i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.1170 | − | 11.0372i | −0.674625 | − | 0.389495i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.11170 | + | 15.1336i | 0.109537 | + | 0.532729i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5613 | − | 11.2937i | 0.687739 | − | 0.397066i | −0.115026 | − | 0.993363i | \(-0.536695\pi\) |
0.802764 | + | 0.596296i | \(0.203362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.9366i | 1.47259i | 0.676659 | + | 0.736296i | \(0.263427\pi\) | ||||
−0.676659 | + | 0.736296i | \(0.736573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.67573 | + | 9.76522i | 0.304271 | + | 0.342481i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.67892 | − | 11.5682i | 0.233666 | − | 0.404721i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.2858 | − | 8.57161i | −1.33781 | − | 0.299516i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.447025 | − | 0.258090i | −0.0156013 | − | 0.00900741i | 0.492179 | − | 0.870494i | \(-0.336201\pi\) |
−0.507780 | + | 0.861487i | \(0.669534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.8125 | + | 10.2841i | −0.620906 | + | 0.358480i | −0.777222 | − | 0.629227i | \(-0.783372\pi\) |
0.156316 | + | 0.987707i | \(0.450038\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0587 | −0.836603 | −0.418301 | − | 0.908308i | \(-0.637374\pi\) | ||||
−0.418301 | + | 0.908308i | \(0.637374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.3074 | − | 22.6941i | 1.36520 | − | 0.788200i | 0.374891 | − | 0.927069i | \(-0.377680\pi\) |
0.990311 | + | 0.138869i | \(0.0443468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.01500 | − | 0.619928i | 0.104589 | − | 0.0215051i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.16117 | + | 39.3574i | −0.282768 | + | 1.36365i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.3158 | − | 6.24984i | −0.460262 | − | 0.216026i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.8758 | 1.37666 | 0.688332 | − | 0.725395i | \(-0.258343\pi\) | ||||
0.688332 | + | 0.725395i | \(0.258343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.33396 | −0.114964 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.8630 | + | 41.7198i | −0.477468 | + | 1.43691i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.47654 | − | 24.1404i | 0.0850949 | − | 0.829474i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.63015 | − | 27.3820i | −0.193226 | − | 0.939748i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.6929 | + | 9.63764i | −0.572225 | + | 0.330374i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9504 | 0.580372 | 0.290186 | − | 0.956970i | \(-0.406283\pi\) | ||||
0.290186 | + | 0.956970i | \(0.406283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.546711 | − | 0.315644i | 0.0186753 | − | 0.0107822i | −0.490633 | − | 0.871366i | \(-0.663235\pi\) |
0.509309 | + | 0.860584i | \(0.329901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.59642 | + | 3.23109i | 0.190947 | + | 0.110243i | 0.592426 | − | 0.805625i | \(-0.298170\pi\) |
−0.401479 | + | 0.915868i | \(0.631504\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.0432 | + | 1.71962i | −0.580832 | + | 0.0586045i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.64782 | + | 6.31821i | −0.124173 | + | 0.215074i | −0.921409 | − | 0.388593i | \(-0.872961\pi\) |
0.797236 | + | 0.603667i | \(0.206295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.6808 | − | 18.3735i | 0.702358 | − | 0.623998i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.53538i | 0.221698i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.5697 | + | 12.4533i | −0.730861 | + | 0.421963i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.9793 | + | 21.6494i | 0.980800 | + | 0.732722i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.7109 | + | 14.8442i | 0.868196 | + | 0.501253i | 0.866748 | − | 0.498746i | \(-0.166206\pi\) |
0.00144772 | + | 0.999999i | \(0.499539\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.6801 | − | 32.1410i | 0.360230 | − | 1.08409i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.6272 | 0.728638 | 0.364319 | − | 0.931274i | \(-0.381302\pi\) | ||||
0.364319 | + | 0.931274i | \(0.381302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.9462i | − | 1.00777i | −0.863771 | − | 0.503884i | \(-0.831904\pi\) | ||
0.863771 | − | 0.503884i | \(-0.168096\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.2160 | − | 5.89821i | −0.343020 | − | 0.198043i | 0.318587 | − | 0.947894i | \(-0.396792\pi\) |
−0.661607 | + | 0.749851i | \(0.730125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.8082 | − | 37.5003i | −0.563728 | − | 1.25772i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.82279 | − | 8.37962i | −0.295574 | − | 0.280728i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.34591 | + | 16.1876i | 0.312749 | + | 0.541697i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.0364 | + | 28.4622i | −1.06966 | + | 0.950324i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.04855 | − | 13.9405i | −0.268434 | − | 0.464942i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.26798 | + | 4.19617i | 0.242131 | + | 0.139795i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.86930 | − | 18.5267i | −0.0622064 | − | 0.616530i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6739 | − | 14.2455i | 0.819284 | − | 0.473014i | −0.0308855 | − | 0.999523i | \(-0.509833\pi\) |
0.850169 | + | 0.526509i | \(0.176499\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.37028 | − | 53.7246i | 0.211289 | − | 1.78193i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4884i | 0.480023i | 0.970770 | + | 0.240011i | \(0.0771511\pi\) | ||||
−0.970770 | + | 0.240011i | \(0.922849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.2571 | − | 19.4979i | −0.372555 | − | 0.645285i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.41831 | + | 23.5728i | −0.0798597 | + | 0.778442i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.83403 | + | 4.90869i | −0.0934861 | + | 0.161923i | −0.908976 | − | 0.416849i | \(-0.863134\pi\) |
0.815490 | + | 0.578772i | \(0.196468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.4333 | + | 6.45748i | 0.640350 | + | 0.212781i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.7200i | 0.550346i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.69854 | + | 0.729323i | −0.0557873 | + | 0.0239541i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.51159 | − | 14.7425i | 0.279256 | − | 0.483686i | −0.691944 | − | 0.721951i | \(-0.743245\pi\) |
0.971200 | + | 0.238265i | \(0.0765788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.8496 | + | 7.21979i | −0.716092 | + | 0.236619i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.79228 | + | 37.8974i | 0.255108 | + | 1.24071i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1936 | 0.365678 | 0.182839 | − | 0.983143i | \(-0.441471\pi\) | ||||
0.182839 | + | 0.983143i | \(0.441471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.2317 | − | 15.3092i | 0.562336 | − | 0.499598i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0101 | − | 19.0700i | −0.358919 | − | 0.621665i | 0.628862 | − | 0.777517i | \(-0.283521\pi\) |
−0.987780 | + | 0.155852i | \(0.950188\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.35513 | + | 16.2036i | −0.304645 | + | 0.527661i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3035 | + | 24.7743i | −0.464800 | + | 0.805057i | −0.999192 | − | 0.0401795i | \(-0.987207\pi\) |
0.534393 | + | 0.845236i | \(0.320540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.3526 | + | 69.8927i | 1.30990 | + | 2.26881i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.8672 | − | 38.9731i | 1.42249 | − | 1.26379i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.2210 | −1.46485 | −0.732426 | − | 0.680846i | \(-0.761612\pi\) | ||||
−0.732426 | + | 0.680846i | \(0.761612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.68181 | − | 13.0429i | −0.0866907 | − | 0.421617i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33.1908 | − | 23.9886i | −1.07179 | − | 0.774631i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.4931 | + | 19.9067i | −0.370746 | + | 0.642150i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 48.8200 | − | 20.9625i | 1.57320 | − | 0.675506i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.5961i | 1.75569i | 0.478943 | + | 0.877846i | \(0.341020\pi\) | ||||
−0.478943 | + | 0.877846i | \(0.658980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.0267 | + | 10.3098i | 0.996722 | + | 0.331200i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1591 | + | 21.0603i | −0.390206 | + | 0.675856i | −0.992476 | − | 0.122436i | \(-0.960929\pi\) |
0.602271 | + | 0.798292i | \(0.294263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.8101 | + | 48.6600i | 0.699198 | + | 1.55997i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.58898 | + | 7.94835i | 0.146815 | + | 0.254290i | 0.930048 | − | 0.367437i | \(-0.119765\pi\) |
−0.783234 | + | 0.621727i | \(0.786431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.8523i | − | 0.698403i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.604246 | − | 5.09599i | 0.0192921 | − | 0.162703i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.3720 | − | 8.29768i | 0.458396 | − | 0.264655i | −0.252974 | − | 0.967473i | \(-0.581409\pi\) |
0.711369 | + | 0.702818i | \(0.248075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.7593 | + | 10.6971i | 0.756268 | + | 0.340491i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.6140 | − | 10.1694i | −0.560092 | − | 0.323369i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.44914 | − | 16.3664i | −0.300162 | − | 0.519895i | 0.676011 | − | 0.736892i | \(-0.263707\pi\) |
−0.976172 | + | 0.216996i | \(0.930374\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.56334 | − | 2.27735i | 0.0813450 | − | 0.0722696i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.37103 | − | 12.7670i | −0.233443 | − | 0.404335i | 0.725376 | − | 0.688353i | \(-0.241666\pi\) |
−0.958819 | + | 0.284018i | \(0.908333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.69414 | + | 19.9380i | 0.0536003 | + | 0.630811i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2100.2.bo.h.1349.9 | 20 | ||
3.2 | odd | 2 | 2100.2.bo.g.1349.5 | 20 | |||
5.2 | odd | 4 | 420.2.bh.a.341.4 | yes | 10 | ||
5.3 | odd | 4 | 2100.2.bi.k.1601.2 | 10 | |||
5.4 | even | 2 | inner | 2100.2.bo.h.1349.2 | 20 | ||
7.3 | odd | 6 | 2100.2.bo.g.1949.6 | 20 | |||
15.2 | even | 4 | 420.2.bh.b.341.5 | yes | 10 | ||
15.8 | even | 4 | 2100.2.bi.j.1601.1 | 10 | |||
15.14 | odd | 2 | 2100.2.bo.g.1349.6 | 20 | |||
21.17 | even | 6 | inner | 2100.2.bo.h.1949.2 | 20 | ||
35.2 | odd | 12 | 2940.2.d.b.881.8 | 10 | |||
35.3 | even | 12 | 2100.2.bi.j.101.1 | 10 | |||
35.12 | even | 12 | 2940.2.d.a.881.3 | 10 | |||
35.17 | even | 12 | 420.2.bh.b.101.5 | yes | 10 | ||
35.24 | odd | 6 | 2100.2.bo.g.1949.5 | 20 | |||
105.2 | even | 12 | 2940.2.d.a.881.4 | 10 | |||
105.17 | odd | 12 | 420.2.bh.a.101.4 | ✓ | 10 | ||
105.38 | odd | 12 | 2100.2.bi.k.101.2 | 10 | |||
105.47 | odd | 12 | 2940.2.d.b.881.7 | 10 | |||
105.59 | even | 6 | inner | 2100.2.bo.h.1949.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.4 | ✓ | 10 | 105.17 | odd | 12 | ||
420.2.bh.a.341.4 | yes | 10 | 5.2 | odd | 4 | ||
420.2.bh.b.101.5 | yes | 10 | 35.17 | even | 12 | ||
420.2.bh.b.341.5 | yes | 10 | 15.2 | even | 4 | ||
2100.2.bi.j.101.1 | 10 | 35.3 | even | 12 | |||
2100.2.bi.j.1601.1 | 10 | 15.8 | even | 4 | |||
2100.2.bi.k.101.2 | 10 | 105.38 | odd | 12 | |||
2100.2.bi.k.1601.2 | 10 | 5.3 | odd | 4 | |||
2100.2.bo.g.1349.5 | 20 | 3.2 | odd | 2 | |||
2100.2.bo.g.1349.6 | 20 | 15.14 | odd | 2 | |||
2100.2.bo.g.1949.5 | 20 | 35.24 | odd | 6 | |||
2100.2.bo.g.1949.6 | 20 | 7.3 | odd | 6 | |||
2100.2.bo.h.1349.2 | 20 | 5.4 | even | 2 | inner | ||
2100.2.bo.h.1349.9 | 20 | 1.1 | even | 1 | trivial | ||
2100.2.bo.h.1949.2 | 20 | 21.17 | even | 6 | inner | ||
2100.2.bo.h.1949.9 | 20 | 105.59 | even | 6 | inner | ||
2940.2.d.a.881.3 | 10 | 35.12 | even | 12 | |||
2940.2.d.a.881.4 | 10 | 105.2 | even | 12 | |||
2940.2.d.b.881.7 | 10 | 105.47 | odd | 12 | |||
2940.2.d.b.881.8 | 10 | 35.2 | odd | 12 |